First Order ODE

Solving first order ODE was introduced in 1st semester. This section extends upon it.

Exact Differential Equation

Suppose and are continuous functions in a region .

A differential equation of the form is exact if such that:

Then is the general solution.

Exact Equation

is an exact equation iff:

Integrating Factor

If the differential equation is not exact, it might be possible to make it exact by multiplying it with its integrating factor .

If the below function is a function of only:

Then .

If the below function is a function of only:

Then .